Others who return from this year’s run could be former Minnesota Gov. Tim Pawlenty, Texas Gov. Ricky Perry and former U.S Sen. Rick Santorum.

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TAMPA, FLA. — When asked who should be next in line should Mitt Romney win or lose the election for president this year, U.S. House Speaker John Boehner pointed to the man sitting to his right – U.S. Sen. Rob Portman.

Portman, R-Terrace Park, tried to deflect Boehner’s response, without denying his interest, by saying the speaker might be the logical choice.

The West Chester Republican would have none of it. “No way,” Boehner said.

Also on some people’s list: Ohio Gov. John R. Kasich, who ran for president in 2000; he dropped out long before the Iowa caucuses and endorsed George W. Bush.

As Republicans meet to nominate their 2012 choice, Mitt Romney, speculation inevitably turns to 2016 – or even 2020. And in those races, Ohio is in the unusual position of having two possible national contenders.

Kasich is getting a lot of attention across the country from Republicans impressed with what he has done in his first two years at the helm. Ohio’s unemployment rate is lower than the national average and has gained 100,000 jobs in the last year.

Kasich said there is no reason not to run for re-election in 2014, which would keep him visible nationally.

But he played down any run for president while speaking to Ohio reporters Tuesday morning in Tampa at the Republican National Convention. Kasich said he’s “at the top of the mountain” as governor. He kidded the reporters, saying, “I don’t want to be here” at the convention.

“This is not my first rodeo,” the governor said. “I have no real interest” in president.

Kasich and Boehner addressed the convention Tuesday night. Portman will do so tonight. That attention is not only a recognition of the importance of Ohio in any presidential election, but it increases the visibility of all three.

Kasich and Portman said they are not visiting other state delegations, which future presidential candidates would typically do to introduce themselves to people in places where they are less known. But the media attention that both are receiving could help a future run. Esquire magazine is doing a story about Kasich, and he is getting overwhelmed by requests from the national news media for interviews.

There’s even a Tampa billboard, sponsored by the Evangelical Environmental Network, which seems to support the policies of both Kasich and New Jersey Gov. Chris Christie, another possible presidential contender. The billboard with Kasich’s picture on it along the highway from the Ohio delegation hotel to the convention center downtown uses a quote from Kasich saying global warming has an impact on the environment. The network’s website says it is a “ministry dedicated to the care of God’s creation.”

Most news reports had Portman as a top finalist for the vice presidential slot on the ticket, but Romney chose U.S. Rep. Paul Ryan of Wisconsin instead. Whether Romney wins or loses, Ryan also is sure to be a top contender in the future.

For Democrats, Portman appears to be the more formidable threat.

Ohio Democratic Party chairman Chris Redfern told The Enquirer Tuesday that Portman has a more moderate and disciplined demeanor.

“Rob Portman is incredibly talented as a politician,” he said. “He understands you cannot iron your blue jeans. He has the temperament that allows him to hide an egregious voting record – as far right as Paul Ryan.”

Kasich, Redfern said, is less disciplined and more partisan. Even in one of the best election years for Republicans in a generation, Kasich failed to get a majority of votes in 2010, Redfern noted.

While Ohio Republicans tend to be supportive of both Kasich and Portman, the difficulty for both could be getting recognized on a broader national scale by rank-and-file Republicans.

“It will be who has the most money,” said Beth Sabatino, a delegate from New York. She knew neither Kasich nor Portman.

William Kristol, founder and editor of The Weekly Standard, a conservative magazine, told The Enquirer that Ryan would be the leading candidate to succeed Romney.

Stark County Commissioner Janet Creighton, an alternate delegate at the Tampa convention, called New Jersey Gov. Chris Christie “great.” She was disappointed that Portman didn’t get picked for the ticket by Romney, calling it “a terrible loss for Ohio.” However, Creighton said she doesn’t see him as presidential material.

“I see him as vice president or a cabinet member,” she said.

Ohio Republican Party chairman Bob Bennett put Kasich at the top of his list, but he had others not far behind.

“These governors who are risk takers really care about moving forward,” Bennett told The Enquirer. “Initially, they’re not very popular” but their popularity grows.

He said Indiana Gov. Mitch Daniels excited people early in the 2012 presidential campaign, which could make him a possible candidate after a Romney term or two. But Daniels will leave the governorship to become president of Purdue University, which could lessen political attention on him.